8 15 Quantum Invariants

A1 Invariants.

Weight	Invariant
1	$q^{21}-2q^{19}+q^{17}-2q^{15}+q^{11}+3q^{7}-q^{5}+q^{3}$
2	$q^{58}-2q^{56}-2q^{54}+6q^{52}-2q^{50}-6q^{48}+9q^{46}+q^{44}-9q^{42}+6q^{40}+3q^{38}-6q^{36}-q^{34}+2q^{32}-7q^{28}+2q^{26}+7q^{24}-8q^{22}+10q^{18}-5q^{16}-2q^{14}+6q^{12}-q^{8}+q^{6}$
3	$q^{111}-2q^{109}-2q^{107}+3q^{105}+6q^{103}-2q^{101}-13q^{99}+2q^{97}+18q^{95}+4q^{93}-25q^{91}-13q^{89}+27q^{87}+22q^{85}-27q^{83}-29q^{81}+20q^{79}+35q^{77}-12q^{75}-32q^{73}+7q^{71}+27q^{69}+4q^{67}-21q^{65}-9q^{63}+10q^{61}+17q^{59}-5q^{57}-21q^{55}-7q^{53}+27q^{51}+13q^{49}-30q^{47}-23q^{45}+27q^{43}+27q^{41}-22q^{39}-32q^{37}+12q^{35}+32q^{33}-6q^{31}-23q^{29}-2q^{27}+19q^{25}+7q^{23}-8q^{21}-4q^{19}+4q^{17}+3q^{15}-q^{11}+q^{9}$
4	$q^{180}-2q^{178}-2q^{176}+3q^{174}+3q^{172}+6q^{170}-9q^{168}-13q^{166}+2q^{164}+11q^{162}+30q^{160}-11q^{158}-41q^{156}-22q^{154}+14q^{152}+80q^{150}+22q^{148}-62q^{146}-83q^{144}-27q^{142}+123q^{140}+97q^{138}-31q^{136}-135q^{134}-108q^{132}+102q^{130}+151q^{128}+41q^{126}-124q^{124}-159q^{122}+38q^{120}+138q^{118}+88q^{116}-63q^{114}-137q^{112}-19q^{110}+80q^{108}+92q^{106}-2q^{104}-81q^{102}-57q^{100}+17q^{98}+75q^{96}+49q^{94}-23q^{92}-93q^{90}-46q^{88}+62q^{86}+102q^{84}+34q^{82}-121q^{80}-107q^{78}+32q^{76}+141q^{74}+101q^{72}-112q^{70}-148q^{68}-28q^{66}+124q^{64}+148q^{62}-49q^{60}-133q^{58}-86q^{56}+53q^{54}+136q^{52}+19q^{50}-62q^{48}-83q^{46}-12q^{44}+70q^{42}+38q^{40}-38q^{36}-24q^{34}+16q^{32}+14q^{30}+11q^{28}-5q^{26}-7q^{24}+2q^{22}+q^{20}+3q^{18}-q^{14}+q^{12}$
5	$q^{265}-2q^{263}-2q^{261}+3q^{259}+3q^{257}+3q^{255}-q^{253}-9q^{251}-13q^{249}+2q^{247}+20q^{245}+23q^{243}+6q^{241}-27q^{239}-49q^{237}-33q^{235}+37q^{233}+92q^{231}+71q^{229}-21q^{227}-131q^{225}-155q^{223}-29q^{221}+172q^{219}+255q^{217}+121q^{215}-157q^{213}-369q^{211}-275q^{209}+93q^{207}+447q^{205}+449q^{203}+42q^{201}-464q^{199}-612q^{197}-218q^{195}+403q^{193}+725q^{191}+409q^{189}-288q^{187}-747q^{185}-557q^{183}+129q^{181}+696q^{179}+645q^{177}+23q^{175}-589q^{173}-647q^{171}-147q^{169}+441q^{167}+591q^{165}+229q^{163}-299q^{161}-511q^{159}-260q^{157}+162q^{155}+395q^{153}+289q^{151}-49q^{149}-310q^{147}-287q^{145}-48q^{143}+215q^{141}+319q^{139}+152q^{137}-156q^{135}-340q^{133}-254q^{131}+77q^{129}+394q^{127}+373q^{125}-7q^{123}-426q^{121}-499q^{119}-98q^{117}+448q^{115}+620q^{113}+214q^{111}-413q^{109}-712q^{107}-360q^{105}+339q^{103}+747q^{101}+494q^{99}-202q^{97}-709q^{95}-595q^{93}+27q^{91}+607q^{89}+634q^{87}+132q^{85}-435q^{83}-592q^{81}-272q^{79}+239q^{77}+496q^{75}+313q^{73}-70q^{71}-337q^{69}-309q^{67}-55q^{65}+194q^{63}+240q^{61}+101q^{59}-72q^{57}-154q^{55}-101q^{53}+6q^{51}+77q^{49}+74q^{47}+18q^{45}-27q^{43}-36q^{41}-14q^{39}+4q^{37}+17q^{35}+12q^{33}-q^{31}-4q^{29}-q^{27}-q^{25}+q^{23}+3q^{21}-q^{17}+q^{15}$

A2 Invariants.

Weight	Invariant
1,0	$q^{32}+q^{30}-2q^{28}-q^{26}-2q^{24}-2q^{22}+q^{20}+3q^{16}+q^{14}+q^{12}+2q^{10}-q^{8}+q^{6}$
1,1	$q^{84}-4q^{82}+10q^{80}-20q^{78}+34q^{76}-54q^{74}+74q^{72}-92q^{70}+105q^{68}-104q^{66}+90q^{64}-60q^{62}+18q^{60}+36q^{58}-90q^{56}+142q^{54}-176q^{52}+200q^{50}-202q^{48}+182q^{46}-153q^{44}+96q^{42}-52q^{40}-10q^{38}+48q^{36}-86q^{34}+104q^{32}-104q^{30}+99q^{28}-72q^{26}+62q^{24}-34q^{22}+25q^{20}-10q^{18}+6q^{16}-2q^{14}+q^{12}$
2,0	$q^{80}+q^{78}-q^{76}-4q^{74}-3q^{72}+2q^{70}+q^{68}+3q^{64}+8q^{62}+4q^{60}-3q^{58}+2q^{54}-4q^{52}-6q^{50}-3q^{48}-3q^{46}-6q^{44}-2q^{42}+q^{40}-3q^{38}+6q^{34}+3q^{32}-3q^{30}+4q^{28}+6q^{26}+q^{24}-2q^{22}+3q^{20}+4q^{18}-q^{16}-q^{14}+q^{12}$

A3 Invariants.

Weight	Invariant
0,1,0	$q^{68}-2q^{66}+3q^{62}-6q^{60}+q^{58}+6q^{56}-5q^{54}+4q^{52}+10q^{50}-3q^{48}-q^{46}-q^{44}-7q^{42}-9q^{40}-7q^{38}+q^{36}-q^{34}-2q^{32}+10q^{30}+5q^{28}-4q^{26}+9q^{24}+2q^{22}-3q^{20}+4q^{18}+q^{16}-q^{14}+q^{12}$
1,0,0	$q^{43}+q^{41}+q^{39}-2q^{37}-q^{35}-4q^{33}-2q^{31}-2q^{29}+q^{27}+q^{25}+2q^{23}+3q^{21}+q^{19}+2q^{17}+2q^{13}-q^{11}+q^{9}$

A4 Invariants.

Weight	Invariant
0,1,0,0	$q^{90}+q^{88}-q^{86}-3q^{84}-q^{82}-5q^{78}-4q^{76}+6q^{74}+8q^{72}+3q^{70}+9q^{68}+14q^{66}+5q^{64}-5q^{62}-4q^{60}-9q^{58}-20q^{56}-17q^{54}-7q^{52}-10q^{50}-6q^{48}+9q^{46}+9q^{44}+2q^{42}+7q^{40}+12q^{38}+4q^{36}-q^{34}+4q^{32}+6q^{30}-q^{28}+3q^{24}+q^{22}-q^{20}+q^{18}$
1,0,0,0	$q^{54}+q^{52}+q^{50}+q^{48}-2q^{46}-q^{44}-4q^{42}-4q^{40}-2q^{38}-2q^{36}+q^{34}+q^{32}+3q^{30}+2q^{28}+3q^{26}+q^{24}+2q^{22}+q^{20}+2q^{16}-q^{14}+q^{12}$

B2 Invariants.

Weight	Invariant
0,1	$q^{68}-2q^{66}+4q^{64}-5q^{62}+6q^{60}-7q^{58}+6q^{56}-5q^{54}+2q^{52}-5q^{48}+7q^{46}-11q^{44}+11q^{42}-13q^{40}+11q^{38}-9q^{36}+7q^{34}-2q^{32}+5q^{28}-4q^{26}+7q^{24}-6q^{22}+7q^{20}-4q^{18}+3q^{16}-q^{14}+q^{12}$
1,0	$q^{110}-2q^{106}-2q^{104}+2q^{102}+4q^{100}-q^{98}-6q^{96}-3q^{94}+6q^{92}+6q^{90}-2q^{88}-6q^{86}+q^{84}+8q^{82}+5q^{80}-4q^{78}-3q^{76}+3q^{74}+3q^{72}-5q^{70}-7q^{68}-2q^{66}+2q^{64}-3q^{62}-7q^{60}-3q^{58}+3q^{56}+3q^{54}-4q^{52}-3q^{50}+5q^{48}+9q^{46}-5q^{42}-q^{40}+8q^{38}+6q^{36}-2q^{34}-5q^{32}+q^{30}+4q^{28}+2q^{26}-q^{24}-q^{22}+q^{18}$

D4 Invariants.

Weight	Invariant
1,0,0,0	$q^{94}-2q^{92}+2q^{90}-3q^{88}+4q^{86}-6q^{84}+4q^{82}-5q^{80}+6q^{78}-3q^{76}+4q^{74}+2q^{72}+5q^{70}+6q^{68}-4q^{66}+5q^{64}-10q^{62}+4q^{60}-17q^{58}-16q^{54}+4q^{52}-8q^{50}+5q^{48}-2q^{46}+6q^{44}+7q^{42}+2q^{40}+6q^{38}-2q^{36}+8q^{34}-3q^{32}+6q^{30}-4q^{28}+5q^{26}-q^{24}+2q^{22}-q^{20}+q^{18}$

G2 Invariants.

Weight

Invariant

1,0

$q^{162}-2q^{160}+4q^{158}-6q^{156}+3q^{154}-q^{152}-6q^{150}+14q^{148}-18q^{146}+20q^{144}-12q^{142}-q^{140}+17q^{138}-27q^{136}+34q^{134}-24q^{132}+7q^{130}+10q^{128}-21q^{126}+25q^{124}-16q^{122}+q^{120}+14q^{118}-20q^{116}+12q^{114}-24q^{110}+34q^{108}-36q^{106}+18q^{104}-2q^{102}-24q^{100}+40q^{98}-47q^{96}+34q^{94}-18q^{92}-7q^{90}+25q^{88}-33q^{86}+26q^{84}-9q^{82}-2q^{80}+16q^{78}-17q^{76}+9q^{74}+10q^{72}-21q^{70}+29q^{68}-21q^{66}+6q^{64}+17q^{62}-27q^{60}+33q^{58}-23q^{56}+12q^{54}+2q^{52}-14q^{50}+17q^{48}-14q^{46}+10q^{44}-2q^{42}-q^{40}+3q^{38}-3q^{36}+3q^{34}-q^{32}+q^{30}$